Practice Midsegment Theorem in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half its length.
Picture a triangular picture frame hanging on a wall. Stretch a rubber band between the midpoints of two sides. That rubber band runs perfectly parallel to the bottom of the frame, like a miniature shelf—and it spans exactly half the width. No matter how you reshape the triangle, that halfway connection always mirrors the opposite side at half scale.
Example 1
easyIn \triangle ABC, M is the midpoint of AB and N is the midpoint of AC. If BC = 18, find MN.
Example 2
mediumIn \triangle PQR, M is the midpoint of PQ and N is the midpoint of QR. If MN = 3x - 1 and PR = 4x + 6, find the value of x and the length MN.
Example 3
easyThe midsegment of a triangle has length 14. What is the length of the side parallel to the midsegment?
Example 4
hardIn \triangle ABC, the three midsegments are drawn, dividing the triangle into four smaller triangles. If the area of \triangle ABC is 120 cm², what is the area of each smaller triangle? Justify using the Midsegment Theorem.